Heat the chicken broth in a microwave or on the stovetop; set aside but keep the broth hot.

Toast the pine nuts over low heat in a dry nonstick frying pan. When the nuts are just starting to brown, remove the pan from heat and set aside.

In a Dutch oven or sauce pan that's both wide and deep (I use a 4-quart stock pot), heat the oil and 1 teaspoon of butter. Over medium heat, sauté the onion until translucent (one minute). Stir in the rice, and continue cooking, stirring to coat the rice kernels with the oil and butter, until the rice just begins to brown.

Slide the pan off the heat and add the wine. Stir quickly to incorporate it with the rice, and return the pan to the heat. Turn the burner to low-medium, and add one cup of the stock. Keep the heat just high enough to maintain a simmer in the pan, and stir occasionally until the liquid is absorbed. Add another another cup of stock, and stir occasionally until incorporated. Add the third cup of stock.

Stir in the pesto. When the stock is incorporated, add the final bit of stock, the peas and the pine nuts. Keep stirring, now and then, and when the last bit of stock is incorporated the rice should be tender but not mushy. If you've added all of the stock and the rice is still too chewy, add 1/4 cup of hot water.

Remove the pot from heat, and add the remaining 2 teaspoons of butter. Stir vigorously to distribute the butter evenly. Add half of the parmesan cheese, and stir to incorporate. Taste, and add black pepper and salt (if you've used store-bought stock, you won't need salt).